Regions of Positive Vorticity in Steady Axisymmetric Flow Past a Viscous Spherical Drop

<table>The numerical solution for <svg height="11.825" id="M199" style="vertical-align:-3.276pt" version="1.1" viewbox="0 0 15.4875 11.825" width="15.4875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M393 379q-9 -16 -28 -29q-15 -10 -23 -2q-19 19 -36 19q-21 0 -52 -38q-57 -72 -82 -126l-40 -197q-23 -3 -75 -18l-7 7q49 196 74 335q7 43 -2 43q-7 0 -30 -14.5t-47 -37.5l-16 23q37 42 82 73t67 31q41 0 15 -113l-11 -50h4q41 71 85 117t77 46q29 0 45 -26
q13 -21 0 -43z" id="x1D45F"></path></g>
<g transform="matrix(.012,-0,0,-.012,7.238,11.762)"><path d="M619 482q0 -69 -40.5 -119t-96 -72.5t-118.5 -26.5h-44l-70 20l-31 -151q-14 -67 0.5 -83t89.5 -22l-5 -28h-287l8 28q65 7 81.5 22t29.5 83l79 398q12 56 0.5 70.5t-78.5 20.5l7 28h255q108 0 164 -43t56 -125zM524 478q0 141 -146 141q-25 0 -47 -8q-16 -6 -20.5 -13.5
t-10.5 -39.5l-43 -241q37 -13 83 -13q67 0 125.5 45t58.5 129z" id="x1D443"></path></g>
</svg>, the end point of the region of positive vorticity behind the drop, plotted against Re for a range of values of <svg height="7.9499998" id="M200" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 8.7375002 7.9499998" width="8.7375002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path d="M484 406q0 -21 -22 -38q-10 -7 -18 -1q-15 11 -30 11q-30 0 -77.5 -37t-74.5 -67l79 -168q11 -23 19.5 -34.5t13 -14t10.5 -2.5q9 0 30 17.5t40 42.5l17 -23q-31 -45 -57.5 -69.5t-40.5 -29.5t-31 -5q-18 0 -32 13.5t-35 55.5q-34 71 -69 160q-36 -32 -59 -56
q-12 -27 -36 -158q-44 -7 -77 -15l-5 7l82 349q6 25 -2 25q-16 0 -72 -41l-14 22q44 41 89 69.5t66 28.5q19 0 19 -32q0 -16 -6 -43l-35 -160l146 143q94 92 136 92q20 0 33 -12t13 -30z" id="x1D705"></path></g>
</svg>.</table>

Mathematical Problems in Engineering

fig5

Figure 5

Figure 5: Regions of Positive Vorticity in Steady Axisymmetric Flow Past a Viscous Spherical Drop 